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Simplifying (2 + -1x)(2.6 + -1x) = 0 Multiply (2 + -1x) * (2.6 + -1x) (2(2.6 + -1x) + -1x * (2.6 + -1x)) = 0 ((2.6 * 2 + -1x * 2) + -1x * (2.6 + -1x)) = 0 ((5.2 + -2x) + -1x * (2.6 + -1x)) = 0 (5.2 + -2x + (2.6 * -1x + -1x * -1x)) = 0 (5.2 + -2x + (-2.6x + 1x2)) = 0 Combine like terms: -2x + -2.6x = -4.6x (5.2 + -4.6x + 1x2) = 0 Solving 5.2 + -4.6x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-5.2' to each side of the equation. 5.2 + -4.6x + -5.2 + x2 = 0 + -5.2 Reorder the terms: 5.2 + -5.2 + -4.6x + x2 = 0 + -5.2 Combine like terms: 5.2 + -5.2 = 0.0 0.0 + -4.6x + x2 = 0 + -5.2 -4.6x + x2 = 0 + -5.2 Combine like terms: 0 + -5.2 = -5.2 -4.6x + x2 = -5.2 The x term is -4.6x. Take half its coefficient (-2.3). Square it (5.29) and add it to both sides. Add '5.29' to each side of the equation. -4.6x + 5.29 + x2 = -5.2 + 5.29 Reorder the terms: 5.29 + -4.6x + x2 = -5.2 + 5.29 Combine like terms: -5.2 + 5.29 = 0.09 5.29 + -4.6x + x2 = 0.09 Factor a perfect square on the left side: (x + -2.3)(x + -2.3) = 0.09 Calculate the square root of the right side: 0.3 Break this problem into two subproblems by setting (x + -2.3) equal to 0.3 and -0.3.Subproblem 1
x + -2.3 = 0.3 Simplifying x + -2.3 = 0.3 Reorder the terms: -2.3 + x = 0.3 Solving -2.3 + x = 0.3 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.3' to each side of the equation. -2.3 + 2.3 + x = 0.3 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + x = 0.3 + 2.3 x = 0.3 + 2.3 Combine like terms: 0.3 + 2.3 = 2.6 x = 2.6 Simplifying x = 2.6Subproblem 2
x + -2.3 = -0.3 Simplifying x + -2.3 = -0.3 Reorder the terms: -2.3 + x = -0.3 Solving -2.3 + x = -0.3 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.3' to each side of the equation. -2.3 + 2.3 + x = -0.3 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + x = -0.3 + 2.3 x = -0.3 + 2.3 Combine like terms: -0.3 + 2.3 = 2 x = 2 Simplifying x = 2Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.6, 2}
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